Question

Can someone please help to explain this to me? I have been trying to work at it and have spent time watching multiple videos trying to figure it out, but am unable to figure it out. Any help would be much appreciated! Thank you.

Answer 1

The maximum value of C = 3x + 4y under the constraints
`\(x \geq 2\), \(x \leq 5\), \(y \geq 1\), and \(y \leq 6\) is \(C = 33\) when \(x = 5\) and \(y = 6\)`.

To find the maximum value of C = 3x + 4y given the constraints
`\(x \geq 2\), \(x \leq 5\), \(y \geq 1\), and \(y \leq 6\)`, let's analyze the vertices of the feasible region formed by these constraints.

The vertices occur at the intersections of the lines defined by the constraints.

The vertices are:

1. x = 2, y = 1

2. x = 5, y = 1

3. x = 2, y = 6

4. x = 5, y = 6

Now, evaluate C at each of these vertices to find the maximum value.

1. For
`\(x = 2, y = 1\): \(C = 3(2) + 4(1) = 10\)`

2. For
`\(x = 5, y = 1\): \(C = 3(5) + 4(1) = 19\)`

3. For
`\(x = 2, y = 6\): \(C = 3(2) + 4(6) = 26\)`

4. For
`\(x = 5, y = 6\): \(C = 3(5) + 4(6) = 33\)`

Hence, the maximum value of C = 3x + 4y subject to the given constraints is C = 33 when x = 5 and y = 6.

Answer 2

first 1 I think

Explanation: